A filter coupling matrix extraction method based on optimization

Abstract

The present invention relates to a filter coupling matrix extraction method based on optimization, comprising: obtaining scattering parameter values ​​of a microwave filter with a loaded phase shift; constructing optimization variables and initializing the optimization variables; constructing a weighted objective function according to the optimization variables; obtaining gradient information according to the objective function calculation, optimizing and updating the optimization variables using a Gauss-Newton optimization algorithm according to the gradient information, and extracting the coupling matrix of the microwave filter according to the optimization results of the optimization variables. The filter coupling matrix extraction method based on optimization of the present invention needs to remove the influence of the loaded phase shift, and the extracted coupling matrix has high accuracy and can be used for debugging microwave filters.

Description

Technical Field

[0001] The invention belongs to the field of microwave technology, and in particular relates to a filter coupling matrix extraction method based on optimization. Background Art

[0002] Microwave filters are key components in wireless communication systems, and their performance determines the performance of the entire communication system. Limited spectrum resources make communication systems more demanding on the performance of microwave filters. How to accurately and quickly design filters that meet the specifications has always been a hot topic for scholars. Designing and debugging microwave filters based on coupling matrices is an efficient method, and accurately extracting coupling matrices has important engineering value.

[0003] The analytical method based on rational function approximation (including fitting and interpolation) algorithm is a more common method for extracting the coupling matrix. The analytical method requires the use of rational function fitting or interpolation methods to perform rational function modeling on the network parameter data of the filter (usually the Y parameter), and then calculates the lateral topological coupling matrix through the Y parameter, and finally rotates and simplifies it to obtain the coupling matrix corresponding to the target topology.

[0004] However, the extraction method of coupling matrix based on analytical method has the following problems: 1. The actual tested / simulated network parameter data contains the phase shift caused by the transmission line at the port and the high-order mode in the external coupling structure, which belongs to the response of the distributed parameter structure and cannot be described by the coupling matrix. Therefore, these additional phase shifts need to be removed in advance when extracting, and the response of the distributed parameter structure and the lumped parameter structure in the network parameters is difficult to distinguish; 2. In the process of rational function modeling of network parameter data, S 21 / Y 21 The zero point is the transmission zero point. When the order of the numerator polynomial is inconsistent with the denominator polynomial, it is very difficult to fit or interpolate the rational function with inconsistent orders of the numerator and denominator polynomials; 3. Due to the influence of factors such as dispersion and parasitics, the circuit cannot accurately correspond to the structure. It is necessary to increase the order of the rational function to obtain a better fitting effect. It is difficult to handle rational functions that are inconsistent with the actual model order; 4. After obtaining the lateral coupling matrix, it is difficult to rotate the matrix to a suitable topological structure according to the position of the transmission zero point, especially the position of the parasitic transmission zero point. Due to these problems, the analytical method has the advantage of fast speed in dealing with the problem of coupling matrix extraction, but the performance is not stable enough, and the scope of use is limited. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a filter coupling matrix extraction method based on optimization. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0006] The present invention provides a filter coupling matrix extraction method based on optimization, comprising:

[0007] Step 1: Obtain the scattering parameter value of the microwave filter with loaded phase shift;

[0008] Step 2: Construct optimization variable x = [M pp ,M pq ], and initialize the optimization variable x; wherein,

[0009] M pp represents all the self-coupling coefficients of the microwave filter, M pq represents all non-zero mutual coupling coefficients of microwave filters;

[0010] Step 3: constructing a weighted objective function according to the optimization variable x and the scattering parameters of the microwave filter without the influence of the loading phase shift;

[0011] Step 4: Obtain gradient information according to the objective function calculation, optimize and update the optimization variable x using the Gauss-Newton optimization algorithm according to the gradient information, and extract the coupling matrix of the microwave filter according to the optimization result of the optimization variable x.

[0012] Compared with the prior art, the present invention has the following beneficial effects:

[0013] 1. The filter coupling matrix extraction method based on optimization of the present invention proposes that the addition of weights in the objective function can appropriately amplify the impact of small signals. Since the optimization goal is to minimize the least squares error, the addition of these weights can avoid the important information contained in the small signal from being ignored.

[0014] 2. The filter coupling matrix extraction method based on optimization of the present invention can optimize and extract the coupling matrix of any topological structure by using the Gauss-Newton optimization algorithm, which is simpler than other methods for extracting the coupling matrix.

[0015] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the following specifically cites a preferred embodiment and describes it in detail with the accompanying drawings as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a schematic diagram of a filter coupling matrix extraction method based on optimization provided by an embodiment of the present invention;

[0017] Figure 2 is a topological structure diagram of a microwave filter provided by an embodiment of the present invention;

[0018] Figure 3 The simulated filter circuit with loaded phase shift provided by the embodiment of the present invention is a simulated S parameter and coupling matrix calculation and an S parameter curve with loaded phase shift added and its phase comparison diagram;

[0019] Figure 4 The simulated S parameter and coupling matrix of the filter circuit with loaded phase shift provided by the embodiment of the present invention are calculated and the S parameter curve and phase comparison diagram of the S parameter curve with loaded phase shift are added;

[0020] Figure 5 It is a simulated fifth-order coaxial cavity filter provided by an embodiment of the present invention;

[0021] Figure 6 The embodiment of the present invention provides a simulation Figure 5 The S parameter curve and phase contrast diagram of the fifth-order coaxial cavity filter simulation and coupling matrix calculation with the addition of loading phase shift are shown;

[0022] Figure 7 For Figure 5 The S parameters of the fifth-order coaxial cavity filter simulation shown are imported into CST to obtain the imported S parameters and analyzed S parameter curves and their phase contrast diagrams. DETAILED DESCRIPTION

[0023] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, a filter coupling matrix extraction method based on optimization proposed in accordance with the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0024] The above and other technical contents, features and effects of the present invention are clearly presented in the following detailed description of the specific implementation modes in conjunction with the accompanying drawings. Through the description of the specific implementation modes, the technical means and effects adopted by the present invention to achieve the predetermined purpose can be more deeply and specifically understood. However, the attached drawings are only for reference and explanation purposes and are not used to limit the technical solutions of the present invention.

[0025] Embodiment 1

[0026] See also Figure 1 , Figure 1 is a schematic diagram of a filter coupling matrix extraction method based on optimization provided by an embodiment of the present invention. As shown in the figure, the filter coupling matrix extraction method based on optimization of this embodiment includes:

[0027] Step 1: Obtain the scattering parameter value of the microwave filter with loaded phase shift;

[0028] Specifically, step 1 includes:

[0029] Simulate the microwave filter using AWR or HFSS simulation software to obtain the scattering parameter value of the microwave filter with loaded phase shift; or connect the microwave filter to a vector network analyzer to obtain the scattering parameter value of the microwave filter with loaded phase shift;

[0030] In this embodiment, the scattering parameters are S parameters, including S 21 and S 11 .

[0031] Step 2: Construct the optimization variable x and initialize the optimization variable x;

[0032] Specifically, step 2 includes:

[0033] Step 2.1: Determine the order of the microwave filter, and construct an N+2 order all-zero coupling matrix of the microwave filter according to the order of the microwave filter, wherein N represents the order of the microwave filter;

[0034] In this embodiment, the N+2-order all-zero coupling matrix can be expressed as M=zeros(N+2,N+2), where zeros(N+2,N+2) represents an N+2×N+2 all-zero matrix.

[0035] Step 2.2: setting an initial value of the coupling coefficient according to the topological structure of the microwave filter, initializing an N+2 order all-zero coupling matrix according to the initial value of the coupling coefficient, and obtaining an initial coupling matrix;

[0036] It should be noted that the coupling coefficient of microwave filters includes self-coupling coefficient and mutual coupling coefficient. Figure 2 , Figure 2 is a topological structure diagram of a microwave filter provided by an embodiment of the present invention, such as Figure 2 The microwave filter shown in the figure has a self-coupling coefficient including M 11 、M 22 、M 33 、M 44 and M 55 , the mutual coupling coefficient includes M s1 、M 12 、M 23 、M 34 、M 45 and M 5L .

[0037] Step 2.3: Set the quality factor;

[0038] The quality factor is obtained by simulating the eigenmode of the resonant cavity of the microwave filter or by comparing the extracted-test / simulation S 21 The curve is obtained.

[0039] It should be noted that port 1 and port 2 represent the input and output of the microwave filter respectively. Since the loss analysis of the microwave filter is reflected in the network function as the offset of the complex frequency variable, that is, s loss =jω+δ, where ω is the low-pass prototype angular frequency, is the loss factor, FBW is the relative bandwidth of the microwave filter, and Q is the quality factor. In this embodiment, the loss factor can be directly optimized as an optimization variable.

[0040] Step 2.4: Construct optimization variable x = [M pp ,M pq ], and initialize the optimization variable x according to the initial coupling matrix.

[0041] In this embodiment, M pp represents all the self-coupling coefficients of the microwave filter, M pq represents all non-zero mutual coupling coefficients of the microwave filter.

[0042] Optionally, in the constructed optimization variable x, the sequential coupling coefficient is in the front and the cross coupling coefficient is in the back.

[0043] Step 3: Construct a weighted objective function based on the optimization variable x and the scattering parameters of the microwave filter that removes the influence of the loading phase shift;

[0044] Specifically, step 3 includes:

[0045] Step 3.1: Sampling the scattering parameter value of the microwave filter with the loaded phase shift to obtain the sampled scattering parameter;

[0046] Step 3.2: Remove the influence of loading phase shift from the sampled scattering parameters to obtain the scattering parameters without the influence of loading phase shift, denoted as S 21S and S 11S , and set the weight of the scattering parameter term in the objective function;

[0047] In this embodiment, optionally, the loading phase shift of the actual parameter can be approximately calculated by using a loading phase shift formula and an optimization method, so as to remove the influence of the loading phase shift and obtain the scattering parameter without the influence of the loading phase shift.

[0048] In this embodiment, S 21 The weight of the parameter item is S 11 The weights of the parameters are

[0049] Where i = 1, 2, 3, ..., N p , N p Indicates the number of sampling frequency points, ω iIt represents the low-pass prototype angular frequency corresponding to the sampling frequency, and j represents the imaginary unit.

[0050] Step 3.3: Construct the node admittance matrix and obtain the calculated scattering parameters based on the node admittance matrix, denoted as S 21M and S 11M ;

[0051] Specifically, the low-pass-bandpass projection expression is defined as:

[0052]

[0053] Among them, ω i Represents the low-pass prototype angular frequency corresponding to the sampling frequency, i=1,2,3,…,N p , N p Indicates the number of sampling frequency points, f i represents the sampling frequency, f0 represents the center frequency, and FBW represents the relative bandwidth of the microwave filter.

[0054] Furthermore, the node admittance matrix is ​​[A] = [G] + jω[C] + j[M], where [G] represents the N+2-order port admittance matrix, [G] 1,1 =[G] N+2,N+2 =1, the rest of the elements are 0, [C] represents the N+2 order node capacitance matrix, which is [C] 1,1 =[C] N+2,N+2 =0 identity matrix.

[0055] In this embodiment, considering the microfilter loss, the node admittance matrix is ​​defined as [A]=[G]+(jω+δ)[C]+j[M].

[0056] Furthermore, according to the node admittance matrix [A], the calculated scattering parameter S is obtained according to the following formula: 21M and S 11M They are:

[0057]

[0058]

[0059] Step 3.4: Construct a weighted objective function based on the scattering parameters without the effect of the loading phase shift, the weights of the scattering parameter terms, and the calculated scattering parameters.

[0060] In this embodiment, the objective function is:

[0061]

[0062]

[0063] Where W21 (jω i ) indicates S 21 The weight of the parameter term, W 11 (jω i ) indicates S 11 The weight of the parameter term, ω i It represents the low-pass prototype angular frequency corresponding to the sampling frequency, and j represents the imaginary unit.

[0064] Step 4: Obtain gradient information based on the objective function calculation. Based on the gradient information, the Gauss-Newton optimization algorithm is used to optimize and update the optimization variable x. Based on the optimization result of the optimization variable x, the coupling matrix of the microwave filter is extracted.

[0065] Specifically, step 4 includes:

[0066] Step 4.1: Calculate the gradient information by using the chain rule of derivation according to the objective function, denoted as J(x), where J(x) includes the first-order derivatives of each element in f(x) at the low-pass prototype angular frequency corresponding to each sampling frequency point with respect to different parameters in the optimization variable x;

[0067] In this embodiment, the self-coupling coefficient M is solved with respect to the S parameter. pp and the mutual coupling coefficient M pq The formula for the first-order partial derivative of is as follows:

[0068]

[0069]

[0070]

[0071]

[0072] Step 4.2: Initialize the parameters of the Gauss-Newton optimization algorithm and set the iteration end condition;

[0073] In this embodiment, the parameters for initializing the Gauss-Newton optimization algorithm include setting a parameter ε for the iteration termination condition;

[0074] The iteration end condition is f(x new )-f(x)<εor k=k max , where k represents the current iteration number, k max Represents the maximum number of iterations, and the initial k is defined as 0.

[0075] Step 4.3: Let k = k + 1, and according to the formula (J T J)h gn =-Jf to find hgn The least squares solution of new =x+h gn ;

[0076] Step 4.4: Determine whether f(x new )-f(x)<ε, if it exists, update the coupling matrix and exit the loop;

[0077] Otherwise, new gradient information is obtained according to the optimization result of the optimization variable x, and the coupling matrix is ​​not updated and optimized;

[0078] It should be noted that, in this embodiment, a new objective function is constructed according to the optimization result of the optimization variable x, so that new gradient information is obtained according to the new objective function.

[0079] Step 4.5: Determine whether the current iteration meets the iteration end condition.

[0080] If satisfied, the optimization algorithm is terminated, and the coupling coefficient matrix of the microwave filter is extracted according to the optimization result of the optimization variable x;

[0081] Specifically, according to the optimization result of the optimization variable x, all the self-coupling coefficients M of the microwave filter in the optimization variable x are extracted. pp And all non-zero mutual coupling coefficients M of microwave filters pq The value of is assigned to the corresponding position in the coupling matrix to the coupling coefficient matrix of the microwave filter.

[0082] If not satisfied, repeat steps 4.3 to 4.5 to optimize and update the optimization variable x.

[0083] In the filter coupling matrix extraction method based on optimization of this embodiment, the addition of weights in the proposed objective function can appropriately amplify the impact of small signals. Since the optimization goal is to minimize the least squares error, the addition of these weights can prevent important information contained in the small signal from being ignored.

[0084] The filter coupling matrix extraction method based on optimization in this embodiment is applicable to all gradient-based optimization algorithms for the objective function of the coupling matrix optimization problem. The coupling matrix of any topological structure can be optimized and extracted based on the Gauss-Newton optimization algorithm. The extraction parameters are highly accurate and simpler than other methods for extracting the coupling matrix.

[0085] Embodiment 2

[0086] This embodiment illustrates the technical effect of the filter coupling matrix extraction method based on optimization in Embodiment 1 through simulation experiments.

[0087] In order to demonstrate the effectiveness of the high precision of the coupling matrix extraction method of the first embodiment of the present invention, the present embodiment carried out a circuit experiment with a loaded phase shift and performed parameter extraction on a 5th-order coaxial cavity filter, compared the scattering parameter response curve of the actual simulation of the microwave filter with the scattering parameter response curve with a loaded phase shift corresponding to the extracted coupling coefficient, and compared the coupling coefficient extracted by using the commonly used simulation software CST with the coupling coefficient extracted by the present embodiment, thereby demonstrating that the method of the present invention can accurately extract the coupling coefficient matrix of the microwave filter.

[0088] The technical effect of this example method is explained below through simulation and experiments.

[0089] 1. Simulation conditions:

[0090] Experimental environment: MATLAB R2021a, AWR simulation software, HFSS simulation software, CST simulation software.

[0091] The method of the present invention is verified by using a 5th order Chebyshev filter, whose topology is as follows: Figure 2 Specifically, the center frequency of the filter is set to 228MHz, and the bandwidth is set to 8MHz, that is, the relative bandwidth is 0.0351. The initial values ​​of the coupling coefficients used for extraction are: M 11 =0,M 22 =0,M 33 =0,M 44 =0,M 55 =0,M S1 =1,M 12 =0.865,M 23 =0.6357,M 34 =0.6357,M 45 =0.865,M 5L =1.

[0092] First, conduct a circuit experiment and set the impedance of the two ports to 50 ohms.

[0093] 2. Simulation content and results

[0094] Simulation 1, the added phase shift is: 20 degrees at 228MHz for 50 ohm transmission line at port 1, 20 degrees for ideal phase shifter; 25 degrees at 228MHz for 50 ohm transmission line at port 2, 13 degrees for ideal phase shifter. The coupling coefficient is set to: M 11 =0.02,M 22 =0.5,M 33 =0.2,M 44 =-0.3,M 55 =0.3,M S1 =1.1,M 12=0.6,M 23 =0.7,M 34 =0.2,M 45 =1.1,M 5L =1.3. The Q value is set to 1200. The coupling matrix extracted by the method of the present invention is as follows:

[0095]

[0096] The coupling coefficient matrix extracted from the filter circuit simulation is plotted as an S-parameter curve with a loaded phase shift, and compared with the actual simulated response curve. Figure 3 As shown, Figure 3 Figure (a) is a simulation of a filter circuit with a phase shift using the method of the present invention. 21 , S 11 Parameters and coupling matrices are calculated and the phase shifted S is added 21 , S 11 Parameter curve comparison chart, Figure 3 Figure (b) is a simulation of a filter circuit with a phase shift using the method of the present invention. 21 , S 11 The phase and coupling matrices of the parameters are calculated and added to the phase shifted S 21 , S 11 Phase contrast plot of the parameters.

[0097] from Figure 3 It can be seen that the Gauss-Newton algorithm has a very small deviation in parameter extraction for the fifth-order filter circuit and can accurately extract the parameters.

[0098] Simulation 2, the added phase shift is: 12 degrees at 228MHz for 50 ohm transmission line at port 1, 12 degrees for ideal phase shifter; 35 degrees at 228MHz for 50 ohm transmission line at port 2, 35 degrees for ideal phase shifter. The coupling coefficient is set to: M 11 =0.2,M 22 =-0.2,M 33 =0.2,M 44 =-0.2,M 55 =0.2,M S1 =1,M 12 =0.6M 23 =0.4,M 34 =0.3,M 45 =1.1,M 5L =1.3. The Q value is set to 120. The coupling matrix extracted by the method of the present invention is as follows:

[0099]

[0100] The coupling coefficient matrix extracted from the filter circuit simulation 2 is plotted as an S parameter curve with a loaded phase shift, and compared with the actual simulated response curve. Figure 4 As shown, Figure 4 Figure (a) is a simulation of a filter circuit with a phase shift using the method of the present invention. 21 , S 11 Parameters and coupling matrices are calculated and the phase shifted S is added 21 , S 11 Parameter curve comparison chart, Figure 4 Figure (b) is a simulation of a filter circuit with a phase shift using the method of the present invention. 21 , S 11 The phase and coupling matrices of the parameters are calculated and added to the phase shifted S 21 , S 11 Phase contrast plot of the parameters.

[0101] from Figure 4 It can be seen that the Gauss-Newton algorithm has a very small deviation in parameter extraction for the fifth-order filter circuit and can accurately extract the parameters.

[0102] In simulation 3, a fifth-order coaxial cavity filter is optimized and extracted. The Q value is set to 4500, and the coupling coefficient matrix is ​​extracted using CST, as shown in Figure 5 The simulated fifth-order coaxial cavity filter shown has a center frequency of 228 MHz and a bandwidth of 8 MHz. The coupling coefficient matrix extracted by the method of the present invention is as follows:

[0103]

[0104] The coupling coefficient matrix extracted using CST is as follows:

[0105]

[0106] The extracted coupling coefficient matrix is ​​plotted as an S-parameter curve with a loaded phase shift and compared with the actual simulated response curve. Figure 6 As shown, Figure 6 Figure (a) is a simulation of a fifth-order coaxial cavity filter using the method of the present invention. 21 , S 11 Parameters and coupling matrices are calculated and the phase shifted S is added 21 , S 11 Parameter curve comparison chart, Figure 6 Figure (b) is a simulation of a fifth-order coaxial cavity filter using the method of the present invention. 21 , S 11 The phase and coupling matrices of the parameters are calculated and added to the phase shifted S 21 , S11 Phase contrast plot of the parameters.

[0107] Please refer to Figure 7 , Figure 7 For Figure 5 The S parameters of the fifth-order coaxial cavity filter simulation shown in the figure are imported into CST, and the imported S parameters and analyzed S parameter curves and their phase comparison diagrams are obtained. The solid line in the figure represents the S parameters analyzed by CST, and the dotted line represents the S parameters imported into CST. Figure 7 Figure (a) is the S imported and analyzed 21 , S 11 Parameter response curve, Figure 7 Figure (b) shows the S imported and analyzed 21 , S 11 The phase of the parameters. It can be seen from the figure that the Gauss-Newton algorithm will have a certain deviation when extracting the parameters of the fifth-order coaxial cavity filter, but it can accurately extract the parameters of the fifth-order cavity filter.

[0108] It should be noted that, in this article, the term "comprises", "comprising" or any other variant is intended to cover non-exclusive inclusion, so that an article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed. In the absence of more restrictions, an element defined by the sentence "comprising a ..." does not exclude the presence of other identical elements in the article or device comprising the element.

[0109] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A filter coupling matrix extraction method based on optimization, It is characterized in that include: Step 1: Obtain the scattering parameter value of the microwave filter with loaded phase shift; Step 2: Construct optimization variable x = [M pp ,M pq ], and initialize the optimization variable x; wherein, M pp represents all the self-coupling coefficients of the microwave filter, M pq represents all non-zero mutual coupling coefficients of microwave filters; Step 3: constructing a weighted objective function according to the optimization variable x and the scattering parameters of the microwave filter without the influence of the loading phase shift; Step 4: Obtaining gradient information according to the objective function calculation, optimizing and updating the optimization variable x using the Gauss-Newton optimization algorithm according to the gradient information, and extracting and obtaining the coupling matrix of the microwave filter according to the optimization result of the optimization variable x; Wherein, the step 3 comprises: Step 3.1: sampling the scattering parameter value of the microwave filter with the loaded phase shift to obtain the sampled scattering parameter; Step 3.2: Remove the influence of the loading phase shift from the sampled scattering parameters to obtain the scattering parameters without the influence of the loading phase shift, denoted as S 21S and S 11S , and set the weight of the scattering parameter term in the objective function; Step 3.3: Construct a node admittance matrix, and obtain the calculated scattering parameters according to the node admittance matrix, denoted as S 21M and S 11M ; Step 3.4: constructing a weighted objective function according to the scattering parameters after removing the influence of the loading phase shift, the weights of the scattering parameter items, and the calculated scattering parameters.

2. The filter coupling matrix extraction method based on optimization according to claim 1, It is characterized in that The step 1 comprises: The microwave filter is simulated by using AWR or HFSS simulation software to obtain the scattering parameter value of the microwave filter with loaded phase shift; or, the microwave filter is connected to a vector network analyzer to obtain the scattering parameter value of the microwave filter with loaded phase shift; The scattering parameters are S parameters, including S 21 and S 11 .

3. The filter coupling matrix extraction method based on optimization according to claim 1, It is characterized in that The step 2 comprises: Step 2.1: Determine the order of the microwave filter, and construct an N+2-order all-zero coupling matrix of the microwave filter according to the order of the microwave filter, wherein N represents the order of the microwave filter; Step 2.2: setting an initial value of the coupling coefficient according to the topological structure of the microwave filter, and initializing the N+2 order all-zero coupling matrix according to the initial value of the coupling coefficient to obtain an initial coupling matrix; Step 2.3: Setting the quality factor, wherein the quality factor is based on the eigenmode simulation of the resonant cavity of the microwave filter or extracted by comparison-test / simulation S 21 The curve is obtained; Step 2.4: Construct the optimization variable x = [M pp ,M pq ], initialize the optimization variable x according to the initial coupling matrix.

4. The filter coupling matrix extraction method based on optimization according to claim 1, It is characterized in that The weight of the scattering parameter term is set according to the following formula, where: S 21 The weight of the parameter item is, S 11 The weight of the parameter item is, Where i = 1, 2, 3, ..., N p , N p Indicates the number of sampling frequency points, ω i It represents the low-pass prototype angular frequency corresponding to the sampling frequency, and j represents the imaginary unit.

5. The filter coupling matrix extraction method based on optimization according to claim 1, It is characterized in that The node admittance matrix is: Where [G] represents the N+2-order port admittance matrix, [G] 1,1 =[G] N+2,N+2 =1, the rest of the elements are 0, [C] represents the N+2 order node capacitance matrix, which is [C] 1,1 =[C] N+2,N+2 =0 unit matrix, [M] represents the coupling matrix, j represents the imaginary unit, ω represents the low-pass prototype angular frequency, δ represents the loss factor, FBW represents the relative bandwidth of the microwave filter, and Q represents the quality factor; The calculated scattering parameters are obtained according to the following formula, where: Where [A] represents the node admittance matrix, and N represents the order of the microwave filter.

6. The filter coupling matrix extraction method based on optimization according to claim 1, It is characterized in that The objective function is: Where W 21 (jω i ) indicates S 21 The weight of the parameter term, W 11 (jω i ) indicates S 11 The weight of the parameter term, ω i It represents the low-pass prototype angular frequency corresponding to the sampling frequency, and j represents the imaginary unit.

7. The filter coupling matrix extraction method based on optimization according to claim 6, It is characterized in that The step 4 comprises: Step 4.1: Calculate the gradient information by using the chain rule of derivation according to the objective function, denoted as J(x), where J(x) includes the first-order derivatives of each element in f(x) at the low-pass prototype angular frequency corresponding to each sampling frequency point with respect to different parameters in the optimization variable x; Step 4.2: Initialize the parameters of the Gauss-Newton optimization algorithm and set the iteration end condition, where: Initializing the parameters of the Gauss-Newton optimization algorithm includes setting the parameter ε for the iteration termination condition; The iteration end condition is f(x new )-f(x)<εor k=k max , where k represents the current iteration number, k max Indicates the maximum number of iterations, and defines the initial k=0; Step 4.3: Let k = k + 1, and according to the formula (J T J)h gn =-Jf Find the least squares solution of hgn, let x new =x+h gn ; Step 4.4: Determine whether f(x new )-f(x)<ε, if it exists, update the coupling matrix and exit the loop; Otherwise, new gradient information is obtained according to the optimization result of the optimization variable x, and the coupling matrix is ​​not updated; Step 4.5: Determine whether the current iteration meets the iteration end condition. If satisfied, the optimization algorithm is terminated, and the coupling coefficient matrix of the microwave filter is extracted according to the optimization result of the optimization variable x; If not satisfied, repeat steps 4.3 to 4.5 to optimize and update the optimization variable x.

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